Delete photos from MacBook Air and store on iCloud
My MacBook Air is really slowing down, how do I store photos on iCloud and delete them from MacBook?
MacBook Air 13″, macOS 10.15
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iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: https://support.apple.com/en-us/HT204264
Apple does not currently offer cloud-only storage for photos. If that is what you want or need, you may want to explore 3rd party options such as Google Photos or Dropbox.
In addition to Optimize Storage and 3rd party cloud options, another option would be to move your photo library to an external drive. See: Move your Photos library to save space on your Mac - Apple Support
Also, unless your Mac storage is very full, having photos in storage shouldn't affect its performance.